15A. The RothCN Model

This chapter is being updated and may contain information that is not yet final.

15A.1. General description

Model structure

The RothCN model is an extension of the well-established RothC model (see RothC Model Description, Rothamsted Research, 2024). It uses the same algorithms as RothC to estimate SOC turnover, and extends the calculation to include SON turnover by introducing C:N ratios to each SOM compartment. During decomposition of SOC compartments, N is released from the decomposing materials, and in the meantime is also assimilated into microbial biomass and humus according to their respective C:N ratios. The difference between N release and assimilation determines whether net mineralization or immobilization takes place.

roth cn schematic
Figure 15A.1: Compartmentalization of soil organic matter pool, partition flows of input materials, and flows of decomposed organic matter between compartments in the RothCN model.

The RothCN model distinguishes organic inputs between plant residues and manure, as the two input types have distinct C:N ratios. Each organic input material is further divided into an easily decomposable and a resistant fraction, depending on their decomposability. Therefore, RothCN maintains four distinct SOM compartments for input materials: DPM & RPM for plant residues, and DMA & RMA for manure. Additionally for manure, a small fraction is assigned for already humified material (HMA). HMA immediately becomes part of HUM once added to soil, therefore it is only considered when partitioning the input material, but not maintained as a separate SOM compartment.

Plant residues (DPM & RPM), manure (DMA & RMA), together with microbial biomass (BIO) and humus (HUM), form the decomposable SOM compartments. In each time step, a fraction of each decomposable compartment decomposes following a first-order reaction kinetics, and converts into BIO, HUM, and CO2. The inert organic matter compartment (IOM) is immune from decomposition.

Time step

RothCN simulates SOM turnover on a monthly time step. If annual output is required, results should be aggregated at the end of each year.

Basic input data requirement

  • Climate data

    • Monthly precipitation (mm).

    • Monthly evapotranspiration (mm).

    • Mean monthly air temperature (°C).

  • Soil data

    • Topsoil thickness (cm).

    • Topsoil clay content (%).

    • Topsoil bulk density (g cm–3).

    • Soil cover: is the soil bare or vegetated in a particular month.

  • Organic input data

    • Monthly input of organic C and N from plant residues (kg C/N ha–1). If only annual input is available, the annual input distributed evenly over 12 months.

    • Monthly input of organic C and N from manure and other organic fertilisers (compost, sludge, etc.; kg C/N ha–1). If only annual input is available, the annual input is distributed evenly over 12 months.

    • An estimate on the fractions of the DPM and RPM compartments in the incoming plant material. If not provided, default values will be used (see Table 15A.1).

    • An estimate on the fractions of the DMA and RMA compartments in the incoming manure material. If not provided, default values will be used (see Table 15A.1).

Parameters

The parameter values given below are default values derived directly from the original RothC and other models, or from literature/empirical values. They may be changed when calibrating the model.

Table 15A.1: Parameters used in RothCN model.
Parameter Description Default value Unit

kDPM

1st-order decomposition rate constant of DPM compartment.

10.0

yr–1

kRPM

1st-order decomposition rate constant of RPM compartment.

0.3

yr–1

kDMA

1st-order decomposition rate constant of DMA compartment.

10.0

yr–1

kRMA

1st-order decomposition rate constant of RMA compartment.

0.3

yr–1

kBIO

1st-order decomposition rate constant of BIO compartment.

0.66

yr–1

kHUM

1st-order decomposition rate constant of HUM compartment.

0.02

yr–1

fDPM

Partition fraction of plant residue C to DPM compartment.

0.59 (annual crops)
0.20 (perennial crops)

fRPM

Partition fraction of plant residue C to RPM compartment.

0.41 (annual crops)
0.80 (perennial crops)

fDMA

Partition fraction of manure and compost/sludge C to DMA compartment.

0.49 (manure)
0.15 (compost/sludge)

fRMA

Partition fraction of manure and compost/sludge C to RMA compartment.

0.49 (manure)
0.70 (compost/sludge)

fHMA

Partition fraction of manure and compost/sludge C to HMA compartment.

0.02 (manure)
0.15 (compost/sludge)

fBIO

Partition fraction of decomposed organic C to BIO compartment.

0.46

fHUM

Partition fraction of decomposed organic C to HUM compartment.

0.54

ψ

Scaling factor to adjust CO2 fraction from decomposed SOC. See Equation 15A.24.

1.670

r'DPM

Theoretical C:N ratio of DPM.

30.0

r'RPM

Theoretical C:N ratio of RPM [2].

100.0

r'DMA

Theoretical C:N ratio of DMA.

18.0

r'RMA

Theoretical C:N ratio of RMA [2].

100.0

r'BIO

Theoretical C:N ratio of BIO.

10.0

r'HUM

Theoretical C:N ratio of HUM.

12.0

r'IOM

Theoretical C:N ratio of IOM.

200.0

15A.2. Algorithms

Determining rate modifying factors

The rate modifying factor is determined for each month of the simulation. Rate modifying factors are calculated following standard RothC approach.

Temperature factor

The rate modifying factor for temperature is given by:

Equation 15A.1

where:

is the rate modifying factor for temperature (unitless).

is the base for natural logarithms, approximately 2.71828.

is the monthly average temperature (°C).

Moisture factor

First, the maximum topsoil moisture deficit (TSMDmax) is calculated:

Equation 15A.2

where:

is the maximum topsoil moisture deficit (mm).

is the percentage of clay content in the soil (%).

is the depth of the soil layer (cm).

Next, the accumulative TSMD (TSMDacc) is calculated. At the beginning of the simulation, TSMDacc is set to 0. Then, in each of the following month:

Equation 15A.3

where:

is the topsoil moisture deficit of the specific month (mm).

is the accumulative topsoil moisture deficit (mm).

is the monthly precipitation surplus (mm).
PS = Monthly Precipitation (mm) − Monthly Evapotranspiration (mm).

is the maximum topsoil moisture deficit (mm). See Equation 15A.2.

And the moisture factor is given by:

Equation 15A.4

where:

is the rate modifying factor for moisture (unitless).

is the maximum topsoil moisture deficit (mm). See Equation 15A.2.

is the accumulative topsoil moisture deficit (mm). See Equation 15A.3.

Soil cover factor

The soil cover factor slows decomposition if growing plants are present.

Equation 15A.5

where is the rate modifying factor for soil cover (unitless).

Combined factor

The final modifying factor is calculated by multiplying all factors:

Equation 15A.6

where:

is the modifying factor for the rate of SOC decomposition (unitless).

is the rate modifying factor for temperature (unitless). See Equation 15A.1.

is the rate modifying factor for moisture (unitless). See Equation 15A.4.

is the rate modifying factor for soil cover (unitless). See Equation 15A.5.

A generic algorithm to partition N

In many calculation cases of the RothCN model, a certain amount of N must be partitioned into several compartments according to the respective C:N ratio of each compartment. As a consequence, the sum of N from relevant compartments estimated using C:N ratios may not match the amount of the available N for partitioning. Here we describe a generic algorithm to partition a fixed amount of N into any number of compartments, while keeping the relative size of each compartment.

The amount of Ntotal is partitioned into n compartments according to the C size (Ci=1…n) and theoretical C:N ratio (r'i=1…n) of each compartment:

Equation 15A.7

If , the provisional size of N compartments (N'i) must be scaled while keeping their relative proportions, i.e., for any compartments i and j:

Equation 15A.8

, and satisfies that .

For any compartment x, solve Nx and rx:

Equation 15A.9

Derivation:

Initialization of soil organic matter pool

Initializing soil organic carbon pool

At the beginning of the simulation period, the initial soil organic carbon pool (SOCinit) is primed based on soil properties:

Equation 15A.10

where:

is the initial content of SOC (kg C ha–1).

is the bulk density of the soil (g cm–3).

is the depth of the soil layer (cm).

is the percentage of SOC content (%).
If soil organic matter content (SOM%) is provided, it may be multiplied by 0.5 to give SOC%.

For compartments DPM, RPM, DMA, and RMA, their respective initial size (Cinit) is calculated assuming a steady state as follows. In the special case where a field has never received organic fertilisers (manure), the initial sizes of CDMA and CRMA should be set to 0.

Equation 15A.11

where:

is the initial content of SOC in compartment i (kg C ha–1).

is the average size of annual C input to compartment i during the simulation period (kg C ha–1 yr–1).

is the average rate modifying factor (unitless) over the simulation period. See Equation 15A.6.

is the first-order decomposition rate constant of compartment i (yr–1).

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA}.
If crop history is available, and should be replaced with corresponding data of the years before the simulation period for better estimation.

The steady state assumes that the C input during a time step is decomposed within the same time step. According to first-order reaction kinetics:

Since dt = 1 (year) and dC = Cin,

The initial size of IOM is estimated according to Falloon et al. (1998). IOM is excluded from SOM decomposition, therefore its size remains the same throughout the simulation.

Equation 15A.12

where:

is the initial content of SOC in the IOM compartment (kg C ha–1).

is the initial content of SOC (kg C ha–1). See Equation 15A.10.
In the original equation, SOC is in tonne C ha–1. Therefore, SOCinit must be converted to tonne C ha–1, and then the result is converted back to kg C ha–1.

After the initial sizes of input materials and IOM pools are determined, the initial sizes of the BIO and HUM pools can be calculated. But first, it should be checked to see if there is enough SOC to fill the BIO and HUM compartments.

Equation 15A.13

If :

If :

where:

is the combined initial content of SOC in the BIO and HUM compartments (kg C ha–1).

is the initial content of SOC in the BIO compartment (kg C ha–1).

is the initial content of SOC in the HUM compartment (kg C ha–1).

is the initial content of SOC (kg C ha–1). See Equation 15A.10.

is the initial content of SOC in compartment i (kg C ha–1). i ∈ {DPM, RPM, DMA, RMA, IOM}. See Equation 15A.11 and Equation 15A.12.

are the first-order decomposition rate constants of the BIO and HUM pool, respectively. See Table 15A.1.

Initializing soil mineral and organic nitrogen pool

For all SOM compartments, the initial sizes of organic N are calculated as:

Equation 15A.14

where:

is the initial content of SON in compartment i (kg N ha–1).

is the initial content of SOC in compartment i (kg C ha–1).

is the theoretical C:N ratio of compartment i (kg C kg–1 N).

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM, IOM}.

If the overall soil C:N ratio is given, an extra step of mass balance check is performed, so that the sum of SON from all compartments matches the size determined from the soil C:N ratio, i.e.:

Equation 15A.15

where:

is the initial content of SON (kg N ha–1).

is the initial content of SON in compartment i (kg N ha–1). See Equation 15A.14.

is the initial content of SOC (kg C ha–1). See Equation 15A.10.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM, IOM}.

If the mass balance check fails, SON sizes in the soil compartments must be adjusted according to Equation 15A.9.

The initial size of soil mineral and organic N pools are finally determined as:

Equation 15A.16

where:

is the initial soil mineral N content (kg N ha–1).

is the initial soil organic N content (kg N ha–1).

is the initial content of SON (kg N ha–1). See Equation 15A.15.
If measurement or estimation on soil mineral N content is available, soil mineral N pool should be primed with the measured or estimated value.

Partitioning of input materials

Partitioning of organic carbon

When an organic input material such as plant residues or manure is added, the organic carbon in the input material is partitioned into relevant compartments according to their respective fractions.

Equation 15A.17

where:

is the organic C content partitioned into compartment i from the input material (kg C ha–1).

is the total organic C content in the input material (kg C ha–1).

is the partition fraction of individual compartment i in the input material (unitless). See Table 15A.1.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, HMA}.

Partitioning of organic nitrogen

The size of organic nitrogen partitioned into each compartment is provisionally determined by the size of organic C and the theoretical C:N ratio.

Equation 15A.18

where:

is the provisional organic N content partitioned into compartment i (kg N ha–1).

is the organic C content in compartment i of the input material (kg C ha–1). See Equation 15A.17.

is the theoretical C:N ratio for compartment i (kg C kg–1 N). See Table 15A.1.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, HMA}.

Then, Equation 15A.9 is used to ensure that the sum of partitioned N matches the actual N content in the input materials. This balance check is performed separately for plant residues and manure:

Equation 15A.19

Decomposition of organic carbon

Decomposition of an organic carbon compartment is simulated on a monthly time step. The size of the compartment at the beginning of the month is equal to the size at the end of the previous month, plus any additional input.

The following convention to denote a time interval is used throughout the sections below:

  • Subscript t0 denotes the starting point of the interval,

  • Subscript t denotes the end point of the interval,

  • Subscript t – 1 denotes the end point of the previous time interval.

Equation 15A.20

where:

is the organic C content (kg C ha–1) in compartment i at time t0, or t−1.

is the monthly organic C input (kg C ha–1) to compartment i .

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, HUM}.
HMA from manure input is added into HUM.

The decomposition follows a first order reaction kinetics. The size of the compartment at the end of the month is given by:

Equation 15A.21

where:

is the organic C content (kg C ha–1) in compartment i at time t, or t0.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

is the base for natural logarithms, approximately 2.71828.

is the combined rate modifying factor ( Equation 15A.6),

is the yearly 1st order decomposition rate constant (yr–1) for compartment i. See Table 15A.1.

is 1/12, since k is a yearly decomposition rate.

Therefore, the amount of decomposed C is:

Equation 15A.22

where:

is the amount of decomposed organic C (kg C ha–1) in compartment i.

is the organic C content (kg C ha–1) in compartment i at time t, or t0. See Equation 15A.20 and Equation 15A.21.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.
The symbol δ denotes decomposed material.

Decomposed organic carbon from all compartments is summed up to give the overall SOC decomposition:

Equation 15A.23

where:

is the total amount of decomposed SOC (kg C ha–1) in all soil compartments.

is the amount of decomposed organic C (kg C ha–1) in compartment i. See Equation 15A.22.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

A fraction of δSOC is lost as CO2, and the rest remains in the soil (Cremain), and is assimilated by microorganisms (BIO) or converted to humus (HUM). The ratio of δSOC lost as CO2 to those remained in soil (μ) is determined by the clay content of the soil:

Equation 15A.24

where:

is the ratio of decomposed organic C lost as CO2 to those remained in soil (unitless).

is the amount of decomposed organic C emitted as CO2 (kg C ha–1).

is the amount of decomposed organic C remained in the soil (kg C ha–1).

is a scaling factor with a default value of 1.67 (unitless) for Rothamsted soil (based on 23.4% clay).

is the base for natural logarithms, approximately 2.71828.

is the percent clay content in the soil (%).

Therefore, the fraction of CO2 emission is , and the fraction of remains in the soil and is assimilated into BIO and HUM compartments by a ratio of 0.46 and 0.54, respectively.

Equation 15A.25

where:

is the amount of decomposed organic C emitted as CO2 (kg C ha–1).

is the amount of decomposed organic C assimilated into the BIO or HUN compartment (kg C ha–1).

is the total amount of decomposed SOC (kg C ha–1) in all soil compartments. See Equation 15A.23.

is the ratio of decomposed organic C lost as CO2 to those remained in soil (unitless). See Equation 15A.24.

is the partition fraction of decomposed organic C into the BIO or HUM compartment. See Table 15A.1.

Decomposition of organic nitrogen

Monthly mineral N input is added to soil mineral N pool at the beginning of the month.

Equation 15A.26

where:

is the soil mineral N content (kg N ha–1) at time t0, or t−1.

is the monthly mineral N input (kg N ha–1).

Monthly organic N input is added to the relevant compartments at the beginning of the month.

Equation 15A.27

where:

is the organic N content (kg N ha–1) in compartment i at time t0, or t−1.

is the monthly organic N input (kg N ha–1) to compartment i.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, HUM}.
HMA from manure input is added into HUM.

Soil organic N pool is also updated with monthly additions:

Equation 15A.28

where:

is the soil organic N content (kg N ha–1) at time t0, or t−1.

is the monthly organic N input (kg N ha–1) to compartment i.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, HUM}.

After input addition, the actual C:N ratio of each compartment is determined:

Equation 15A.29

where:

is the actual C:N ratio (kg C kg–1 N) in compartment i.

is the amount of organic C (kg C ha–1) in compartment i at time t0. See Equation 15A.20.

is the amount of organic N (kg N ha–1) in compartment i at time t0. See Equation 15A.27.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

If the field has never received manure input (i.e. DMA and RMA = 0), this could lead to a division-by-zero error. Set r values of the corresponding compartments to NaN to avoid it.

After the determination of decomposed organic C in each compartment, N released during decomposition is calculated:

Equation 15A.30

where:

is the amount of organic N released from decomposition (kg C ha–1) in compartment i.

is the amount of decomposed organic C (kg C ha–1) in compartment i. See Equation 15A.22.

is the actual C:N ratio (kg C kg–1 N) in compartment i. See Equation 15A.29.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

The size of the N pool at the end of the month (Nt) is determined by:

Equation 15A.31

where:

is the organic N content (kg N ha–1) in compartment i at time t, or t0. See Equation 15A.27.

is the amount of organic N released from decomposition (kg C ha–1) in compartment i. See Equation 15A.30.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

The total N released from decomposition is:

Equation 15A.32

where:

is the total amount of organic N released from decomposition (kg C ha–1) in all soil compartments.

is the amount of organic N released from decomposition (kg C ha–1) in compartment i. See Equation 15A.30.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

δSON is further assimilated by BIO and HUM. The potential amount assimilated into each compartment is calculated as:

Equation 15A.33

where:

is the provisional amount of organic N (kg N ha–1) assimilated into compartment i.

The apostrophe ( ) denotes that this value is provisional and may subject to further adjustment, as described in Immobilization.

is the amount of decomposed SOC (kg C ha–1) assimilated into compartment i. See Equation 15A.25.

are the theoretical ( Table 15A.1) and actual C:N ratios ( Equation 15A.29) of the compartment (kg C kg–1 N), respectively. The lesser of the two values is used to maximize N assimilation.

is the respective compartment, BIO or HUM.

The difference between total N released from decomposition, and the N requirement for assimilation, is calculated:

Equation 15A.34

where:

is the difference between total N released from decomposition, and the N requirement for assimilation (kg N ha–1). Ndiff may be positive or negative.

is the total amount of organic N released from decomposition (kg N ha–1) in all soil compartments. See Equation 15A.32.

is the provisional amount of organic N (kg N ha–1) assimilated into the BIO or HUM compartment. See Equation 15A.33.

Mineralization

If Ndiff > 0, then net mineralization takes place. Ndiff is added to soil mineral N pool as inorganic N, and the corresponding amount is subtracted from soil organic N pool.

Equation 15A.35

where:

is the amount of soil mineral N (kg N ha–1).

is the amount of soil organic N (kg N ha–1).

is the difference between total N released from decomposition, and the N requirement for assimilation (kg N ha–1). See Equation 15A.34.

Immobilization

If Ndiff < 0, immobilization must take place to satisfy the N requirement by BIO and HUM assimilation. As soil microorganisms must compete with plants for N, immobilization is not able to utilize the entire soil mineral N pool. A coefficient is applied to derive the mineral N available for immobilization.

Equation 15A.36

where:

is the amount of soil mineral N (kg N ha–1) available for immobilization.

is the amount of soil mineral N (kg N ha–1).

is an arbitrary parameter with a default value of 0.8 (unitless).
Full immobilization

If Nimmobilizable ≥ |Ndiff|, all N requirement for immobilization can be fulfilled. The amount of |Ndiff| is deducted from soil mineral N and added to organic N pool.

Equation 15A.37

where:

is the final amount of N assimilation (kg N ha–1) into the BIO or HUM compartment after adjustement for immobilization.

is the potential N assimilation (kg N ha–1) into the BIO or HUM compartment as calculated in Equation 15A.33.

is the amount of soil mineral N (kg N ha–1).

is the amount of soil organic N (kg N ha–1).

is the absolute value of the difference between total N released from decomposition, and the N requirement for assimilation (kg N ha–1). See Equation 15A.34.
Partial or reduced immobilization

If Nimmobilizable < |Ndiff|, there is no sufficient N for full immobilization. One of two methods may be used to implement immobilization in this case: either N assimilation is partially fulfilled (“partial fulfillment”), or organic matter decomposition is reduced (“deferred decomposition”).

The total immobilized N (Nimmob) can be determined as:

Equation 15A.38

where:

is the amount of N immobilized (kg N ha–1).

is the total amount of organic N released from decomposition (kg N ha–1) in all soil compartments. See Equation 15A.32.

is the amount of soil mineral N (kg N ha–1) available for immobilization. See Equation 15A.36.

The size of soil mineral and organic N pool after immobilization is:

Equation 15A.39

where:

is the amount of soil mineral N (kg N ha–1).

is the amount of soil organic N (kg N ha–1).

is the amount of soil mineral N (kg N ha–1) available for immobilization. See Equation 15A.36.

  • Method 1: Partial fulfillment

  • Method 2: Deferred decomposition

This is the current method implemented in Miterra-Europe.

In this approach, the BIO and HUM compartments will disregard their C:N ratios, and assimilate all immobilizable N. This leads to changes in C:N ratios of the BIO and HUM compartments.

The BIO compartment has priority for N assimilation over HUM. Therefore, Nimmob satisfies assimilation by BIO first, and any remaining part goes into HUM.

Equation 15A.40

where:

is the final amount of N assimilation (kg N ha–1) into the BIO or HUM compartment after adjustement for immobilization.

is the potential N assimilation (kg N ha–1) into the BIO or HUM compartment as calculated in Equation 15A.33.

is the amount of N immobilized (kg N ha–1). See Equation 15A.38.
This approach is currently not implemented. The description given here is so far for reference only.

In this approach, decomposition of organic matter in each soil compartment is reduced. As it is difficult to estimate new decomposition rate constant for each compartment, we opt for a “deferred decomposition” approach. The decomposition rate constants remain unchanged, instead a fraction of the source material is withheld from decomposition in the current time step, and is “deferred” for decomposition until a later iteration, as soon as there is sufficient inorganic N.

  1. The actual N assimilated into BIO and HUM compartments are calculated as:

    Equation 15A.41

    where:

    is the respective compartment, BIO or HUM, and

    is the potential N assimilation calculated by Equation 15A.33.

  2. The actual C assimilated into BIO and HUM compartments can be determined from C:N ratios, following the rearranged form of Equation 15A.33:

    Equation 15A.42

  3. The actual amount of decomposed SOC can be determined using an inverse form of Equation 15A.25:

    Equation 15A.43

  4. The amount of deferred SOC is then calculated as:

    Equation 15A.44

  5. The deferred SOC is partitioned into each compartment as follows:

    Equation 15A.45

    where:

    is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

    Following deferred decomposition, all subsequent C and N calculations from Equation 15A.23 onwards must be rerun to produce new values. With this approach, and should be able to converge in one iteration.

  6. Finally, the deferred C is added to the respective compartment as input in the next time step.

    Equation 15A.46

Annual balance

At the end of the year, all forms of N removal from soil within the year, including gaseous emissions, surface runoff, leaching, and crop removal, are subtracted from soil mineral N pool. Any remaining soil mineral N is assumed to be completely denitrified.

Equation 15A.47

where:

is the amount of soil mineral N (kg N ha–1).

is the total amount of gaseous N emissions (kg N ha–1). See 10.2. Gaseous N emissions.

is the amount of N losses via surface runoff (kg N ha–1). See Surface runoff of N.

is the amount of N leached (kg N ha–1). See N leaching.

is the amount of N removed from soil by harvest (kg N ha–1). See 6.2. Harvested products.

is the amount of N removed from soil by residue removal (kg N ha–1). See 6.4. Residue removal & incorporation.

The annual changes in soil organic C and N pools can be determined as:

Equation 15A.48

where:

are the change in soil organic C (kg C ha–1) and soil organic N (kg N ha–1), respectively.

is the final content of organicc C (kg C ha–1) in compartment i by the end of the simulation, as calculated in Equation 15A.21.

is the final content of organic N (kg N ha–1) in compartment i by the end of the simulation, as calculated in Equation 15A.31.

is the respective compartment, i ∈ {DPM, RPM, DMA, RMA, BIO, HUM}.

is the initial content of SOC (kg C ha–1). See Equation 15A.10.

is the initial content of SON (kg N ha–1). See Equation 15A.15.